The interactive step trade-off method (ISTM) for multiobjective optimization

The interactive step tradeoff method (ISTM) is composed of three basic steps. First, an efficient solution and the corresponding local tradeoff information are provided by the analyst. Then, the decision maker determines the preference direction and step size. Again the analyst looks for a new efficient solution according to the preference information; the new solution should dominate the previous one. In ISTM, the efficient solution and the local tradeoff information, the current values of objective functions, and the tradeoff rates between them are obtained by solving an auxiliary problem. The auxiliary problem is defined, and relationships between the optimal solutions of the auxiliary problem and the efficient solutions of the original problem are explored. The relationships between the Kuhn-Tucker multipliers (or simplex multipliers) of the auxiliary problems and the tradeoff rates are analyzed. The particular steps of the ISTM algorithm are given. An example is discussed to illustrate the use of the algorithm